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Actually it wouldn't if everything started with a diameter of 100,000 light years across (the size of our galazy). Time would be the same for the entire space. Once the universe started expanding then the gravity well would begin decreasing and time would speed up for the outer edged of the universe but time would remain the same for everything in the gravity well. It would still take 50,000 earth years for us to see the light at the edges of the universe.
Permalink Reply by Alexander Martin on November 18, 2010 at 6:54am Upon re-reading the technical paper by Dr. Hartnett, I think I have your answer.
The principle source of time dilation, according to Hartnett is not gravitational, but rather due to the velocity of the expansion of space. Therefore the depth of the gravitaitonal well is not the primary concern, rather, the rate of the expansion of space is of utmost importance. Any gravitational time dilation would simply add to the effect of cosmological expansion.
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